Transcription

2 Front cover: The sculpture "La Porte de l Enfer" by Auguste Rodin. Back cover: The author being glad to have made it down in one piece. This work is part of the research programme of the Stichting voor Fundamenteel Onderzoek der Materie (FOM), which is financially supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO).

9 Chapter 1 Introduction History shows that people are interested in the workings of the world around them. Ancient Greek philosophers are known to have contemplated on the nature of matter which we are made of. Anaxagoras for instance speculated that matter changes by the re-ordering of indivisible particles, which Democritus named atoms. Gathering and formulating proof for such hypotheses was formalised by Aristotle. This was extended by Roger Bacon to the scientific method of empirically observing nature to scrutinise hypotheses. It was not until 1897 that the field of elementary particle physics was born. Joseph J. Thompson discovered the first elementary particle in that year; the electron. Ernest Rutherford inferred the existence of the atomic nucleus from the results of scattering experiments. For the lightest atom, he named the nucleus proton. Protons are found to only form a part of nuclei, as they are combined with neutrons, which were later discovered by Chadwick. The electron, proton and neutron all form matter. Antimatter was discovered by Anderson in the form of the positron. Matter is what the observed universe from stars to interstellar dust is found to be made of. This matter is expected to have been created in equal amounts to antimatter during the Big Bang. So why don t we see antimatter in the world around us? Annihilation reduces the amount of matter and antimatter equally and therefore cannot explain the absence of antimatter. An imbalance in the presence of matter and antimatter can be created when the famous Sakharov conditions are met. One of these is the violation of CP symmetry. The C and P operations together change particles and antiparticles into each-other and reverse all spatial coordinate signs. If nature is not invariant under the CP operation, then particles behave differently from antiparticles, leading to the matter-antimatter imbalance. The study of CP violation is part of the motivation for conducting the LHCb experiment. Elementary particle physics has grown to an understanding of elementary matter on the level of quarks and leptons. The mechanisms behind their strong and electroweak interactions are formulated in a theory known as the Standard Model. The electromagnetic and weak interactions were combined by Glashow, Weinberg and Salam, for which they received the Nobel prize in Chapter 2 introduces the Standard Model, the known elementary particles and gives a description of how CP violation is implemented in this theory. 9

10 10 CHAPTER 1. INTRODUCTION Study of CP violation began in 1964, when it was observed in the decay of neutral kaons. This was expanded on by observing B hadrons as created in particle accelerators like PEP-II at SLAC and Tevatron at Fermilab. In order to improve on those observations, the LHC machine will offer higher centre-of-mass energy and luminosity. The LHC is build at CERN, offering collisions at a centre-of-mass energy 14 TeV to four main experiments. One of these is LHCb, which is described in chapter 3. The unprecedented amount of produced B hadrons will be used by LHCb to study CP violation as well as rare decays in the B meson system. Designing a detector like LHCb offers experimental challenges, for which suitable solutions must be found. The design process benefits from existing knowledge of particle interactions and the performance of detector hardware. This understanding is used to predict the properties of the collisions and the response of the detector to the ensuing particles and radiation. Monte-Carlo software, as introduced in chapter 4, offers the possibility to simulate a working experiment and quantify the impact of design choices on the performance of the detector. The simulated detector response is used in the development of software strategies, which aim at reconstructing the particles that traverse the detector from measured data. A particle can move through the entire detector or only part of it and be detected by all traversed sensitive layers or move undetected through for instance a structural support section of a layer. These aspects are taken into account when identifying hits in sensitive layers as being due to a single particle. The identification process is split into several pattern recognition strategies, which are described in chapter 5. Given the hits that the pattern recognition ascribes to an individual particle, the path of that particle through the detector is determined by fitting a track model to those hits. The fitting process takes the impact of the traversed material and the magnetic field into account and results in a track. This reconstructed track offers the optimal estimate of the position and momentum of a particle, as well as their covariances, throughout the detector. In chapter 6 the fitting process and its tuning are detailed. The performance of the track fit is evaluated in chapter 7. The reconstructed tracks are used in a multitude of physics analyses. There, a track is combined with the energy and type of the corresponding particle, as provided by the calorimeter system, particle identification detectors, and muon chambers. From this information the event can be reconstructed. In the final chapter, the impact of the track parameter resolution on the reconstructed invariant mass, and on the proper time is illustrated. This shows the importance of high quality track reconstruction.

11 Chapter 2 Theory The established particle physics theory is summarised in the Standard Model of elementary particles and interactions. An introduction to the Standard Model is given in section 2.1. The description of CP violation is included in the Standard Model, where it appears in weak charged-current interactions, and is discussed in section 2.2. The mixing and decay of B mesons and all three types of CP violation are detailed in section 2.3. More comprehensive descriptions of the Standard Model, CP violation and the decay modes of interest to LHCb can be found in the literature [1, 2]. 2.1 The Standard Model The field of particle physics is defined by the study of elementary particles and their interactions. Experimental and theoretical efforts to study these subjects have culminated in a theory known as the Standard Model. It describes elementary particles interacting through the electromagnetic, weak and strong forces. The descriptions and predictions of the Standard Model are compatible with experimental results. One open issue is the predicted existence of the Higgs boson(s) [3], which is expected to be verified at the LHC. A shortcoming of the Standard Model is formed by the fact that the values of 18 of its parameters must be determined by experiments, rather than by fundamental considerations. Finally, the Standard Model describes three out of the four fundamental forces of nature. The exclusion of gravity from this theory prevents it to be a complete theory of (astro-)particle physics. Elementary particles are sorted into fermions and bosons. They are distinguished from each other by the value of their spin. Fermions have a half-integer spin and bosons have an integer spin. Fermions interact through the electromagnetic and weak forces, as detailed in the Glashow-Salam-Weinberg (GSW) model, and through the strong force as described by Quantum Chromodynamics (QCD). In both models, the origin of interactions is related to symmetries of the physics under gauge transformations. These invariances predict the existence of mediating force carriers, which are exchanged between fermions. The fundamental forces, their relative strengths and mediating gauge bosons are listed in table

12 12 CHAPTER 2. THEORY Table 2.1: The fundamental forces of the Standard Model, their relative strengths and mediating gauge bosons [4]. force relative strength gauge bosons strong O(1) 8 gluons (g i ) electromagnetic O(10 2 ) photon (γ) weak O(10 6 ) weak bosons (W ±, Z 0 ) The elementary fermions are separated into quarks and leptons, which have some of their properties stated in table 2.2. They exist in particle and antiparticle variants, which have identical masses and lifetimes, while all internal quantum numbers are of the opposite sign. A splitting into three generations of fermions is made. Each generation consists of two quarks and two leptons, whose masses increase from the first to the third generation. The six quarks interact through all fundamental forces, having mass, electric charge, weak isospin and colour charge. Left-handed quarks and leptons are separated into up-type and down-type by the third component of their weak isospin (T z ). The up, charm and top quarks and neutral leptons have T z one-half and the down, strange and bottom quarks and charged leptons have T z minus one-half. Right-handed quarks and leptons have zero weak isospin and do not interact weakly. Leptons partake in all but strong interactions, as they have no colour charge. The electron, muon and tau leptons have integer electric charges and are paired with neutral leptons called neutrinos. Table 2.2: Properties of the elementary fermions of the Standard Model [4]. The (anti-)quarks exist in three (anti-)colours and antiparticles have the opposite electric charge. type generation name elec. charge mass lepton quark electron(e) MeV electron neutrino(ν e ) 0 < 3 ev muon(µ) MeV muon neutrino(ν µ ) 0 < 0.19 MeV tau(τ) GeV tau neutrino(ν τ ) 0 < 18.2 MeV up(u) 2/ MeV down(d) -1/3 4-8 MeV charm(c) 2/ GeV strange(s) -1/ MeV top(t) 2/ GeV bottom(b) -1/ GeV Another difference between quarks and leptons became apparent by the observation that quarks do not exist as free particles in nature. All quarks but the top

13 2.2. CP VIOLATION IN THE STANDARD MODEL 13 are combined into composite particles called hadrons. The top quark decays before hadronisation can take place. The restriction to hadrons is known as confinement, and is due to the strong force between quarks. This strong interaction is described by QCD, which is based on the SU(3) C gauge symmetry group. It dictates the existence of eight gauge bosons, known as gluons. These gluons are massless vector bosons, which couple to colour charge, and themselves also have colour charges. Hadrons are colour-neutral pairs (mesons) or triplets (hadrons) of red, green, and blue quarks and anti-red, anti-green, and anti-blue antiquarks, bound together by gluon exchanges. At distances smaller than the size of a hadron, the strength of the strong force decreases towards zero with the distance between the component quarks. This phenomenon of asymptotic freedom enables the quarks in high-energy collisions to be considered as free particles, simplifying their theoretical treatment. In the Standard Model, the electromagnetic and weak forces are treated as a single electroweak interaction, which is described by the GSW model. This theory is based on the SU(2) L U(1) Y symmetry group. Given the fact that the W and Z bosons have masses, this is not an exact symmetry. Their non-zero masses imply breaking of the gauge invariance of the electroweak theory, leading to nonrenormalisability, if it was not for the Higgs mechanism [3, 5]. In that scheme, the theory itself is gauge invariant, but the ground state does not exhibit the symmetry, a feature known as spontaneous symmetry breaking. Spontaneous symmetry breaking allows fermions to acquire mass from the Yukawa coupling to the Higgs field. Quark mass eigenstates are not weak eigenstates, those are given by superpositions of the quark mass eigenstates. These superpositions are described by the Cabibbo-Kobayashi-Maskawa [6, 7] (CKM) quark mixing matrix. The electromagnetic force is mediated by a massless gauge boson called the photon. It is exchanged by particles with an electric charge. The weak force has two charged gauge bosons (W ± ) with a mass of 80.40±0.03 GeV [4] and one neutral gauge boson (Z 0 ) of ±0.002 GeV [4]. In a weak interaction, the W ± and Z 0 bosons are virtual particles, which limits the effective range of the weak force to around m. The photon on the other hand is massless, offering infinite range to the electromagnetic force. Comparing the two forces within the effective range of the weak force reveals that their strengths are of the same order of magnitude. 2.2 CP violation in the Standard Model Neither charge conjugation C, nor parity P nor their combined operation CP are conserved symmetries in weak decays. Particles are not eigenstates of C, unless they are their own antiparticle. Parity violation was first observed in the β decay of 60 Co in 1957 [8]. The violation of CP symmetry was discovered through the study of K L ππ decays in 1964 [9]. CP violation has also been observed in decays of neutral B d mesons in 2001 [10, 11]. The origin of CP violation in the Standard Model is embedded in the flavour structure of weak charged-current interactions. These interactions convert up-type quarks into a superposition of down-type quarks, through the emission or absorption of a W ±, and similarly down-type quarks into a

15 2.2. CP VIOLATION IN THE STANDARD MODEL 15 quark fields, keeping one overall phase. This leaves four parameters which need to be determined experimentally, being three rotation angles and one complex phase. This complex phase is the source of CP violation in the Standard Model weak interactions [7]. In case a pair of up-type or down-type quarks from two generations have equal mass, the complex phase can be eliminated through a unitary transformation of the quark fields [13]. The CKM matrix can also be written in the Wolfenstein expansion [14] of four free parameters. It is based on the observation that the diagonal elements are close to unity and the off-diagonal elements are progressively smaller. Transitions between the first and second generations are suppressed by CKM factors of first order, suppression increases by an order for transitions between the second and third generations and between the first and third generations the suppression is of O(10 3 ). The matrix elements are expanded up to third order around the sine of the Cabibbo angle λ = sin θ C [15] as follows: λ2 λ Aλ 3 (ρ iη) V CKM = λ λ2 Aλ 2 + O(λ4 ). (2.3) Aλ 3 (1 ρ iη) Aλ 2 1 In this expansion, the parameters A, ρ and η are real numbers. As the complex phase is the source of observed CP violation, the parameter η is expected to be non-zero. Terms up to O(λ 5 ) in the Wolfenstein expansion are required for the study of physics channels in for instance the B s sector. The additional terms are [14]: 1 8 λ4 0 0 A 2 λ 5 ( 1 ρ iη) λ4 (1 + 4A 2 ) Aλ5 (ρ + iη) Aλ 4 ( 1 ρ iη) + O(λ6 ). (2.4) A2 λ 4 The unitarity of the CKM matrix provides nine constraining relations between the matrix elements. Three of these constraints can be formulated as Σ j V i j 2 = 1 for each generation i. This states that the sum of all couplings of an up-type quark to each of the down-type quarks is identical for each of the generations and is known as weak universality. The other six relations are orthogonality conditions and can be written as Σ k V ik V jk = 0 (i j). Three relations define the orthogonality of the columns and the remaining three that of the rows of the CKM matrix. They are given as follows: V ud V us + V cd V cs + V td V ts = 0, (2.5) V us V ub + V csv cb + V tsv tb = 0, (2.6) V ud V ub + V cdv cb + V tdv tb = 0, (2.7) V ud V cd + V usv cs + V ub V cb = 0, (2.8) V cd V td + V csv ts + V cb V tb = 0, (2.9) V ud V td + V usv ts + V ub V tb = 0. (2.10) Each of these relations can be represented by a triangle in the complex plane [16]. All six triangles have different shapes, but equal surfaces. Their surface is equal to

17 2.3. THE B MESON SYSTEM 17 The three internal angles α, β and γ are re-phasing invariant observables. They are specified in terms of CKM matrix elements as: ( α = arg V tdv ) tb V ud V ub ( β = arg V cdv ) cb V td V tb ( γ = arg V udv ) ub V cd V cb with world-averaged values [17] as stated in table 2.5.,,, (2.13) Table 2.5: World-averaged values of the unitarity triangle angles α, β and γ. observable value ± 3σ [ ] α β γ The Standard Model description of CP violation can be tested by determining the elements of the CKM matrix. Measuring the angles and lengths of the sides of all of the triangles over-constrains the CKM matrix. This offers the possibility to find hints of new physics if inconsistency is observed between the constraints. The existing measurements relating to the angles α, β and γ, predominantly made by the BaBar, Belle, CDF and D0 experiments, have been translated into contour constraints in the ρ, η plane, as shown in figure 2.2. They include direct measurements of the CP phases α, β, and γ by the B-factory experiments, as for instance sin 2β in the B 0 d J/ψK s channel [19, 20]. The circle contours around (1,0) originate from the measured oscillation frequencies of the B d (BaBar and Belle) and B s (CDF and D0) mesons. Circle contours around (0,0) represent V ub, and the hyperbole comes from ɛ in the kaon system. 2.3 The B meson system B mesons are composed of a b antiquark and a u, d, s or c quark, forming a B + u, B 0 d, B0 s or B + c. Together with the anti-b mesons, there are four neutral and four charged mesons making up the B meson system. According to the CPT theorem, each meson and corresponding anti-meson have the same mass and lifetime. The first discovered B meson is the B 0 d, which was observed by the CLEO [21] and CUSB [22] collaborations in In 1983, the MAC [23] and MARK-II [24] collaborations were the first to measure B meson lifetimes. The mean lifetime of B 0 d and B0 s mesons is 1.5 ps, allowing for a fraction of their decay vertices to be observed separately from the primary interaction vertex.

PX434 Physics of the Standard Model Dr Steven Boyd : P448 ATLAS Event Display Intro Stuff Lectures are divided in chapters each chapter has a writeup which will be put online There is a module homepage

Chapter 16 Constituent Quark Model Quarks are fundamental spin- 1 particles from which all hadrons are made up. Baryons consist of three quarks, whereas mesons consist of a quark and an anti-quark. There

Weak Interactions: towards the Standard Model of Physics Weak interactions From β-decay to Neutral currents Weak interactions: are very different world CP-violation: power of logics and audacity Some experimental

Beyond the Hype: The Status of the ATLAS Experiment and the Large Hadron Collider at CERN Kenneth Johns University of Arizona A Dream LHC Schedule LHC (Large Hadron Collider) 3 First Beam in the LHC September

1 Anomalies and the Standard Model The Glashow-Weinberg-Salam model of the electroweak interactions has been very successful in explaining a wide range of experimental observations. The only major prediction

The LHCb Tracking System Jeroen van Hunen The LHCb Experiment LHCb at Point 8 : a lot of activity! LHCb : a B-physics experiment that is being constructed for : Precision measurements of the CPviolation

Information about the T9 beam line and experimental facilities The incoming proton beam from the PS accelerator impinges on the North target and thus produces the particles for the T9 beam line. The collisions

Nuclear Composition - the forces binding protons and neutrons in the nucleus are much stronger (binding energy of MeV) than the forces binding electrons to the atom (binding energy of ev) - the constituents

PHYSICS WITH LHC EARLY DATA ONE OF THE LAST PROPHETIC TALKS ON THIS SUBJECT HOPEFULLY We may have some two month of the Machine operation in 2008 LONG HISTORY... I will extensively use: Fabiola GIANOTTI

The Standard Model or Particle Physics 101 Nick Hadley Quarknet, July 7, 2003 Thanks Thanks to Don Lincoln of Fermilab who provided some of the pictures and slides used in this talk. Any errors are mine

Introduction The Cathode Ray Tube or Braun s Tube was invented by the German physicist Karl Ferdinand Braun in 897 and is today used in computer monitors, TV sets and oscilloscope tubes. The path of the

The Super Era of Sub-Atomic Particle Physics Jay Hauser Abstract: Particle physics has now moved into the "Super" era, in which Supersymmetry, Supergravity, and Superstring theories will be investigated

Top rediscovery at ATLAS and CMS on behalf of ATLAS and CMS collaborations CNRS/IN2P3 & UJF/ENSPG, LPSC, Grenoble, France E-mail: julien.donini@lpsc.in2p3.fr We describe the plans and strategies of the

Pearson Physics Level 30 Unit VIII Atomic Physics: Chapter 17 Solutions Student Book page 831 Concept Check Since neutrons have no charge, they do not create ions when passing through the liquid in a bubble

Flavour Physics Tim Gershon University of Warwick 31 March 2014 Outline Lecture 1 what is flavour physics? some history, some concepts, some theory charged lepton physics What is flavour physics? Parameters

Using the M 2 and variables to investigate Monte Carlo methods of t t production Caitlin Jones September 8, 25 Abstract In this project the behaviour of Monte Carlo simulations for the event t t! ` `+b

1 Searching for the Building Blocks of Matter Building Blocks of Matter The Smallest Scales Physicists at Fermilab are searching for the smallest building blocks of matter and determining how they interact

Chapter Relativity II. Selected Problems.1 Problem.5 (In the text book) Recall that the magnetic force on a charge q moving with velocity v in a magnetic field B is equal to qv B. If a charged particle

hij Teacher Resource Bank GCE Physics A Other Guidance: Particle Physics By J Breithaupt Copyright 2008 AQA and its licensors. All rights reserved. The Assessment and Qualifications Alliance (AQA) is a

Adiabatic Expansion From the Friedmann equations, it is straightforward to appreciate that cosmic expansion is an adiabatic process: In other words, there is no ``external power responsible for pumping

Homework #8 203-1-1721 Physics 2 for Students of Mechanical Engineering Part A 1. Four particles follow the paths shown in Fig. 32-33 below as they pass through the magnetic field there. What can one conclude

[ Assignment View ] [ Pri Eðlisfræði 2, vor 2007 28. Sources of Magnetic Field Assignment is due at 2:00am on Wednesday, March 7, 2007 Credit for problems submitted late will decrease to 0% after the deadline

Part II, 3. Energy measurement in calorimeters 3.1 Concept of a calorimeter in particle physics 3.2 Interactions of photons with matter 3.3 Electromagnetic and hadronic showers 3.4 Layout and readout of

[ Assignment View ] [ Eðlisfræði 2, vor 2007 27. Magnetic Field and Magnetic Forces Assignment is due at 2:00am on Wednesday, February 28, 2007 Credit for problems submitted late will decrease to 0% after

Lecture Outlines Chapter 27 Astronomy Today 7th Edition Chaisson/McMillan Chapter 27 The Early Universe Units of Chapter 27 27.1 Back to the Big Bang 27.2 The Evolution of the Universe More on Fundamental

1 1 Introduction Cosmology is the study of the universe as a whole, its structure, its origin, and its evolution. Cosmology is soundly based on observations, mostly astronomical, and laws of physics. These

The Early Universe Lecture 27-1 Back to the Big Bang The total energy of the universe consists of both radiation and matter. As the Universe cooled, it went from being radiation dominated to being matter

STUDY OF THE DEPENDENCE OF THE WIRE TENSION AS A FUNCTION OF TEMPERATURE FOR A DRIFT TUBE OF THE ATLAS MUON SPECTROMETER Activity report Student: Nicolò Spagnolo, Liceo Scientifico Farnesina, Roma Tutors:

Physics 1653 Exam 3 - Review Questions 3.0 Two uncharged conducting spheres, A and B, are suspended from insulating threads so that they touch each other. While a negatively charged rod is held near, but

Introduction: what is quantum field theory? Asaf Pe er 1 January 13, 2015 This part of the course is based on Ref. [1] 1. Relativistic quantum mechanics By the mid 1920 s, the basics of quantum mechanics

Calorimeter alignmnt and calibration in ILD Executive summary We summarize here the answers of ILD to the questions raised by IDAG regarding the calorimeter alignment and calibration. We present calibration

Calorimeters The energy of hadrons, pions, photons and electrons can be measured with calorimeters. This in contrast with muons: their momentum is measured from their track curvature (sagitta). The principle

Chapter 4 Calibration The accurate calibration of all detectors is crucial for the subsequent data analysis. The stability of the gain and offset for energy and time calibration of all detectors involved

Development of Radiation Resistant Quadrupoles Based on High Temperature Superconductors for the Fragment Separator R. Gupta and M.Harrison, Brookhaven National Laboratory A. Zeller, Michigan State University

Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering

5 Particle Physics This lecture is about particle physics, the study of the fundamental building blocks of Nature and the forces between them. We call our best theory of particle physics the Standard Model

To ensure the functioning of the site, we use cookies. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy &amp Terms.
Your consent to our cookies if you continue to use this website.